FACTOR ANALYSIS WITH EXTERNAL CRITERIA APPLICATION OF ANALYSIS OF VARIANCE AND REGRESSION ANALYSIS TECHNIQUE TO FACTOR ANALYSIS

HARUO YANAI

doi:10.4992/psycholres1954.12.143

FACTOR ANALYSIS WITH EXTERNAL CRITERIA

APPLICATION OF ANALYSIS OF VARIANCE AND REGRESSION ANALYSIS TECHNIQUE TO FACTOR ANALYSIS

HARUO YANAI

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1970 Volume 12 Issue 4 Pages 143-153

DOI https://doi.org/10.4992/psycholres1954.12.143

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Published: 1970 Received: November 24, 1970 Available on J-STAGE: February 24, 2009 Accepted: - Advance online publication: - Revised: -
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Date of correction: February 24, 2009 Reason for correction: - Correction: ABSTRACT Details: Wrong : We propose a new technique of factor analysis with external criteria together with its computational procedure.
First of all, we shall discuss some relationships between the principle of analysis of variance and that of regression analysis by introducing the mathematical concept of projection. Secondly, we shall show that two kinds of factors could be extracted, and that one of them would be closely related to the informations concerning the predetermined external criteria and another one would be índependent of them. Thirdly, we shall show that our proposal might give a satisfactory answer to psychological interpretation of factors without assuming rotation of factors and the estimation of communalities. Finally, two numerical examples will be presented.
Right : We propose a new technique of factor analysis with external criteria together with its computational procedure.
First of all, we shall discuss some relationships between the principle of analysis of variance and that of regression analysis by introducing the mathematical concept of projection. Secondly, we shall show that two kinds of factors could be extracted, and that one of them would be closely related to the informations concerning the predetermined external criteria and another one would be independent of them. Thirdly, we shall show that our proposal might give a satisfactory answer to psychological interpretation of factors without assuming rotation of factorsand the estimation of communalities. Finally, two numerical examples will be presented.

Date of correction: February 24, 2009 Reason for correction: - Correction: CITATION Details: Wrong : BURT, S. C. 1966 The appropriate uses of factor analysis and analysis of variance. Cattel, R. C. (Eds.). Handbook of multivariate experimental psychology Chicago: Rand Mcnally, Pp. 267-287.
CRONBACH, L. J. 1951 Coefficient alph and internal structure of tests. Psychometrika. 16, 297-334.
CRONBACH, L. J. & GLESER, G. L. 1965 Gene-ralizability of scores influenced by multiple sources of variance. Psychometrika. 3, 395-420.
EDWARDS, A. L. 1957 The social desirability variable in personality assessment research. New York: The Deyden Press.
GOLLOB, H. F. 1969 A statistical model which combines features of factor analysis and analysis of variance technique. Psychometrika 34, 73-115.
GULLIKSEN, H. 1950 Theory of mental test. New York: Wiley
JONES, L. V. 1966 Analysis of variance in its multivariate development. Cattel, R. C. (Eds.). Handbook of multivariate experimental psychology. Chicago: Rand Mcnally, Pp. 244-265.
TUKEY, J. W. 1962 The future of data analysis. Annals of mathematical statistics, 33, 1-67.
YANAI, H. 1969 Factor analysis of vocational aptitude test: Application of variance analysis technique to factor analysis. Jap. J. educ. Psychol. 17, 1-12 (in Japanese).
YANAI, H., HIDANO, T., NUSHI, A., SHIGEMASU, K., & TAKANE, Y. 1971 A methodological study of the test scale construction. Jap. J. educ. Psychol. 19, 33-47 (in Japanese).

Right : BURT, S. C. 1966 The appropriate uses of factor analysis and analysis of variance. Cattel, R. C.(Eds.). Handbook of multivariate experimental psychology Chicago: Rand Mcnally, pp.267-287.
CRONBACH, L. J. 1951 Coefficient alph and internal structure of tests. Psychometrika. 16, 297-334.
CRONBACH, L. J. & GLESER, G. L. 1965 Generalizability of scores influenced by multiple sources of variance. Psychometrika. 3, 395-420.
EDWARDS, A. L. 1957 The social desirability variable in personality assessment research. New York: The Deyden Press.
GOLLOB, H. F. 1969 A statistical model which combines features of factor analysis and analysis of variance technique. Psychometrika 34, 73-115.
GULLIKSEN, H. 1950 Theory of mental test. New York: Wiley
JONES, L. V. 1966 Analysis of variance in its multivariate development. Cattel, R. C.(Eds.). Handbook of multivariate experimental psychology. Chicago: Rand Mcnally, pp.244-265.
TUKEY, J. W. 1962 The future of data analysis. Annals of mathematical statistics, 33, 1-67.
YANAI, H. 1969 Factor analysis of vocational aptitude test: Application of variance analysis technique to factor analysis. Jap. J. educ. Psychol. 17, 1-12 (in Japanese).
YANAI, H., HIDANO, T., NUSHI, A., SHIGEMASU, K., & TAKANE, Y. 1971 A methodological study of the test scale construction. Jap. J. educ. Psychol. 19, 33-47 (in Japanese).

Date of correction: February 24, 2009 Reason for correction: - Correction: PDF FILE Details: -

Date of correction: February 24, 2009 Reason for correction: - Correction: ABSTRACT Details: Wrong : We propose a new technique of factor analysis with external criteria together with its computational procedure.
First of all, we shall discuss some relationships between the principle of analysis of variance and that of regression analysis by introducing the mathematical concept of projection. Secondly, we shall show that two kinds of factors could be extracted, and that one of them would be closely related to the informations concerning the predetermined external criteria and another one would be independent of them. Thirdly, we shall show that our proposal might give a satisfactory answer to psychological interpretation of factors without assuming rotation of factorsand the estimation of communalities. Finally, two numerical examples will be presented.
Right : We propose a new technique of factor analysis with external criteria together with its computational procedure.
First of all, we shall discuss some relationships between the principle of analysis of variance and that of regression analysis by introducing the mathematical concept of projection. Secondly, we shall show that two kinds of factors could be extracted, and that one of them would be closely related to the informations concerning the predetermined external criteria and another one would be independent of them. Thirdly, we shall show that our proposal might give a satisfactory answer to psychological interpretation of factors without assuming rotation of factors and the estimation of communalities. Finally, two numerical examples will be presented.

Date of correction: February 24, 2009 Reason for correction: - Correction: CITATION Details: Wrong : BURT, S. C. 1966 The appropriate uses of factor analysis and analysis of variance. Cattel, R. C.(Eds.). Handbook of multivariate experimental psychology Chicago: Rand Mcnally, pp.267-287.
CRONBACH, L. J. 1951 Coefficient alph and internal structure of tests. Psychometrika. 16, 297-334.
CRONBACH, L. J. & GLESER, G. L. 1965 Generalizability of scores influenced by multiple sources of variance. Psychometrika. 3, 395-420.
EDWARDS, A. L. 1957 The social desirability variable in personality assessment research. New York: The Deyden Press.
GOLLOB, H. F. 1969 A statistical model which combines features of factor analysis and analysis of variance technique. Psychometrika 34, 73-115.
GULLIKSEN, H. 1950 Theory of mental test. New York: Wiley
JONES, L. V. 1966 Analysis of variance in its multivariate development. Cattel, R. C.(Eds.). Handbook of multivariate experimental psychology. Chicago: Rand Mcnally, pp.244-265.
TUKEY, J. W. 1962 The future of data analysis. Annals of mathematical statistics, 33, 1-67.
YANAI, H. 1969 Factor analysis of vocational aptitude test: Application of variance analysis technique to factor analysis. Jap. J. educ. Psychol. 17, 1-12 (in Japanese).
YANAI, H., HIDANO, T., NUSHI, A., SHIGEMASU, K., & TAKANE, Y. 1971 A methodological study of the test scale construction. Jap. J. educ. Psychol. 19, 33-47 (in Japanese).

Right : BURT, S. C. 1966 The appropriate uses of factor analysis and analysis of variance. Cattel, R. C.(Eds.). Handbook of multivariate experimental psychology Chicago: Rand Mcnally, Pp.267-287.
CRONBACH, L. J. 1951 Coefficient alph and internal structure of tests. Psychometrika. 16, 297-334.
CRONBACH, L. J. & GLESER, G. L. 1965 Generalizability of scores influenced by multiple sources of variance. Psychometrika. 3, 395-420.
EDWARDS, A. L. 1957 The social desirability variable in personality assessment research. New York: The Deyden Press.
GOLLOB, H. F. 1969 A statistical model which combines features of factor analysis and analysis of variance technique. Psychometrika 34, 73-115.
GULLIKSEN, H. 1950 Theory of mental test. New York: Wiley
JONES, L. V. 1966 Analysis of variance in its multivariate development. Cattel, R. C.(Eds.). Handbook of multivariate experimental psychology. Chicago: Rand Mcnally, Pp.244-265.
TUKEY, J. W. 1962 The future of data analysis. Annals of mathematical statistics, 33, 1-67.
YANAI, H. 1969 Factor analysis of vocational aptitude test: Application of variance analysis technique to factor analysis. Jap. J. educ. Psychol. 17, 1-12 (in Japanese).
YANAI, H., HIDANO, T., NUSHI, A., SHIGEMASU, K., & TAKANE, Y. 1971 A methodological study of the test scale construction. Jap. J. educ. Psychol. 19, 33-47 (in Japanese).

Abstract

We propose a new technique of factor analysis with external criteria together with its computational procedure.
First of all, we shall discuss some relationships between the principle of analysis of variance and that of regression analysis by introducing the mathematical concept of projection. Secondly, we shall show that two kinds of factors could be extracted, and that one of them would be closely related to the informations concerning the predetermined external criteria and another one would be independent of them. Thirdly, we shall show that our proposal might give a satisfactory answer to psychological interpretation of factors without assuming rotation of factors and the estimation of communalities. Finally, two numerical examples will be presented.

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